Very long baseline interferometry observations of supernovae and gamma-ray bursts provide almost the only way of obtaining spatially resolved information about the sources. In particular, a determination of the expansion velocity of the forward shock, as well as the geometry of the fireball and its evolution with time are possible for relatively nearby events, provided they are radio bright. Monitoring the expansion of the shock front can provide information on the density profiles of both the circumstellar material and on the ejecta. Very long baseline interferometry observations can also potentially resolve gamma-ray burst jets which are not directed along the line of sight, providing crucial confirmation of relativistic expansion in such objects. This review gives an overview of recent results from supernovae, including the Type I b/c SNe 2011dh, 2009bb, and 2007gr, and discusses the prospects for future observations.

Radio observations play a key role in studying the jets that power GRBs, the most luminous cosmic explosions. They are crucial for determining the GRB jet energy, the external density, and the microphysical parameters of relativistic collisionless shocks, from afterglow broadband modeling. Radio image size measurements are rare, but provide extremely useful information. The “radio flare” peaking after ~1 day helps constrain the magnetisation and magnetic-field structure of GRB outflows. This review discusses the current observational and modeling status, focusing on the afterglow and outlining prompt radio emission searches, along with recent theoretical progress in GRB jet dynamics, focusing on magnetic acceleration, jet propagation inside a massive star progenitor (for long GRBs), the reverse shock, and the late afterglow. Great progress has been made in our understanding of magnetic acceleration, collimation and later sideways expansion of GRB jets, with interesting implications for the prompt, reverse shock, and afterglow emission. We outline how theory and observations were combined to study GRB jet physics and their immediate environment. Finally, potential paths are suggested for combining theory and observations to achieve greater progress, and some prospects for the future are discussed in light of the expected improvements in observational capabilities and theoretical advances.

Many upcoming surveys, particularly in the radio and optical domains, are designed to probe either the temporal and/or the spatial variability of a range of astronomical objects. In the light of these high resolution surveys, we review the subject of ultra-luminous X-ray (ULX) sources, which are thought to be accreting black holes for the most part. We also discuss the sub-class of ULXs known as the hyper-luminous X-ray sources, which may be accreting intermediate mass black holes. We focus on some of the open questions that will be addressed with the new facilities, such as the mass of the black hole in ULXs, their temporal variability and the nature of the state changes, their surrounding nebulae, and the nature of the region in which ULXs reside.

I review the astrophysical insights arising from high-precision astrometric observations of X-ray binary systems, focussing primarily (but not exclusively) on recent results with very long baseline interferometry. Accurate, model-independent distances from geometric parallax measurements can help determine physical parameters of the host binary system and constrain black hole spins via broadband X-ray spectral modelling. Long-term proper motion studies, combined with binary evolution calculations, can provide observational constraints on the formation mechanism of black holes. Finally, the astrometric residuals from parallax and proper motion fits can provide information on orbital sizes and jet physics. I end by discussing prospects for future progress in this field.

Orphan Afterglows (OA) are slow transients produced by Gamma Ray Bursts seen off–axis that become visible on timescales of days/years at optical/NIR and radio frequencies, when the prompt emission at high energies (X and γ rays) has already ceased. Given the typically estimated jet opening angle of GRBs θjet ~ 3°, for each burst pointing to the Earth there should be a factor ~ 700 more GRBs pointing in other directions. Despite this, no secure OAs have been detected so far. Through a population synthesis code we study the emission properties of the population of OA at radio frequencies. OAs reach their emission peak on year-timescales and they last for a comparable amount of time. The typical peak fluxes (which depend on the observing frequency) are of few μJy in the radio band with only a few OA reaching the mJy level. These values are consistent with the upper limits on the radio flux of SN Ib/c observed at late times. We find that the OA radio number count distribution has a typical slope − 1.7 at high fluxes and a flatter ( − 0.4) slope at low fluxes with a break at a frequency–dependent flux. Our predictions of the OA rates are consistent with the (upper) limits of recent radio surveys and archive searches for radio transients. Future radio surveys like VAST/ASKAP at 1.4 GHz should detect ~ 3 × 10− 3 OA deg− 2 yr− 1, MeerKAT and EVLA at 8.4 GHz should see ~ 3 × 10− 1 OA deg− 2 yr− 1. The SKA, reaching the μJy flux limit, could see up to ~ 0.2 − 1.5 OA deg− 2 yr− 1. These rates also depend on the duration of the OA above a certain flux limit and we discuss this effect with respect to the survey cadence.

We investigate the optimal tradeoff between sensitivity and field of view in surveys for slow radio transients using the event detection rate as the survey metric. This tradeoff bears implications for the design of surveys conducted with upcoming widefield radio interferometers, such as the ASKAP VAST survey and the MeerKAT TRAPUM survey. We investigate (i) a survey in which the events are distributed homogeneously throughout a volume centred on the Earth, (ii) a survey in which the events are homogeneously distributed, but are only detectable beyond a certain minimum distance, and (iii) a survey in which all the events occur at an identical distance, as is appropriate for a targetted survey of a particular field which subtends Npoint telescope pointings. For a survey of fixed duration, Tobs, we determine the optimal tradeoff between number of telescope pointings, N, and integration time per field. We consider a population in which the event luminosity distribution follows a power law with index − α, and tslew is the slewing time between fields or, for a drift scan, the time taken for the telescope drift by one beamwidth. Several orders of magnitude improvement in detection rate is possible by optimization of the survey parameters. The optimal value of N for case (i) is Nmax ~ Tobs/4tslew, while for case (iii) we find Nmax = (Lmax/L0)2[(3 − α)/2]2/(α − 1), where Lmax is the maximum luminosity of a transient event and L0 is the minimum luminosity event detectable in an integration of duration Tobs. (The instance Nmax > Npoint in (iii) implies re-observation of fields over the survey area, except when the duration of transient events exceeds that between re-observations of the same field, where Nmax = Npoint applies instead.) We consider the balance in survey optimization between telescope field of view, Ω, and sensitivity, characterised by the minimum detectable flux density, S0. For homogeneously distributed events (i), the detection rate scales as NΩS−3/20, while for targetted events (iii) it scales as NΩS1 − α0. However, if the targetted survey is optimised for N the event detection rate scales instead as ΩS−20. This analysis bears implications for the assessment of telescope designs: the quantity ΩS−20 is often used as the metric of telescope performance in the SKA transients literature, but only under special circumstances is it the metric that optimises the event detection rate.